Theory of high-frequency linear response of isotropic type-II superconductors in the mixed state

A self-consistent approach to vortex dynamics, including the effects of nonlocal vortex interaction, pinning, and creep, is further clarified and unified by its restatement in terms of an initial-boundary value problem. We derive and solve a single vector partial differential equation describing the linear response of a type-II superconductor in the mixed state at frequencies well below the gap frequency. The solution of this equation, presented here for several sample geometries, provides the phenomenological superconductor dispersion relation, accompanying complex penetration depths, and complex response functions. The theory is expected to have applicability to a wide range of experiments involving vortex dynamics